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Make the oxtail stock:
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1. Parboil the oxtails: Place the oxtail sections in a large pot and cover them with cold water. Bring the water to a vigorous boil over high heat and let it continue to boil for 2 to 3 minutes. Drain and rinse the oxtails in clean water. Scrub the pot clean and return the oxtails to the pot. (This step makes a cleaner stock, because it helps remove bits of marrow and other impurities that will cloud the flavor of the stock.)
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2. Make the stock: Add the onion, leek, ginger, head of garlic, and kombu to the pot. Add enough water to cover all the ingredients by 1-inch, and bring the mixture to a slow boil over high heat. Turn the heat to low, and gently simmer, uncovered, for 7 hours, adding water as necessary to keep the oxtails covered.
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3. Remove the oxtails and submerge them in a clean pot of cold water for 10 minutes. Drain the sections and bring them to room temperature, then store them in an airtight container and refrigerate until ready to use.
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4. Discard all the remaining solids, then strain the stock through a sieve lined with cheesecloth into a clean pot. Stir in the coarse sea salt, and let the stock cool at room temperature, then store in the refrigerator overnight to let the flavors develop and the fat separate to the top.
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Make the garlic miso paste:
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1. Stir the miso and crushed garlic cloves together in a small bowl.
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2. In a small skillet, heat the oxtail fat. When it has melted, add the miso mixture, and cook it over low heat, stirring constantly, for 5 minutes. transfer the mixture to a small container, and set it aside until ready to use.
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Make the soft boiled eggs:
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Place the eggs in a saucepan and cover with cold water. Bring the water to a boil over medium-high heat, then cook the cooks for 1 minute 30 seconds. Immediately remove the eggs and rinse them under cold water until they are cool enough to handle. Remove them from the water and pat the shells dry with a kitchen towel. Set the eggs aside until ready to be served (or make ahead of time and keep chilled in the refrigerator, for up to 3 days).
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Assemble the ramen:
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1. Remove the pot of chilled oxtail broth from the refrigerator. Scoop off the white crust of fat, leaving a few bits of it for flavor. Place the pot over medium heat and bring to a rolling boil.
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2. Place 1 tablespoon of the miso garlic paste into each noodle bowl. Drain the cooked noodles and divide them among the bowls. Add some of the shredded oxtail meat. Add 1 to 1 1/2 cups of hot ramen stock to each bowl. With a pair of chopsticks or tongs, lift and stir the noodles several times so that the miso garlic paste dissolves.
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3. Crack each egg shell at the larger end, lightly tapping it on a hard surface. Then carefully peel the shell away. If necessary, use a small spoon to gently scoop the egg from its shell. Carefully slice each egg in half and place on top of the noodles. Drain the scallions and use to garnish. Serve immediately.
